Gaps between primes

This workshop, sponsored by
AIM and the
NSF,
will be devoted to the recent
work of Goldston, Pintz, and Yildirim on gaps between primes and
primes in tuples.
The work depends on a surprisingly effective variation of the Selberg
sieve, and it has connections and applications to other problems in
sieve methods.
We seek participants who are experts in sieve methods as well as
those who are not; in particular, we encourage those who may be unfamiliar
with sieves but have expertise in other areas of number theory to
attend.
The simplicity of the basic ideas should allow the participants to
quickly understand
both what is known and what are the main unresolved questions.
Further applications
and relationships to other areas of number theory will be explored.
The main topics for the workshop are:

Approximations for primes in tuples and
their application to small gaps between primes

Applications of the new approximations to sieve methods,
numbers with few prime factors,
and the parity problem

Open problems such as bounded gaps between primes,
level of distribution of primes in arithmetic
progressions, the relationship between the Elliott-Halberstam
conjecture and the twin prime
conjecture, and further applications to other
problems.

The workshop will differ from typical conferences in some regards.
Participants will be invited to suggest open problems and questions
before the workshop begins, and these will be posted on the workshop
website. These include specific problems on which there is hope of
making some progress during the workshop,
as well as more ambitious problems which may influence
the future activity of the field.
Lectures at the
workshop will be focused on familiarizing the participants with the
background material leading up to specific problems, and the
schedule will include discussion and working sessions.

The deadline to apply for support to participate in this
workshop has passed.